A285386 Lexicographically earliest sequence of distinct positive terms such that the product of two consecutive terms is divisible by p^4 for some prime p.

1, 16, 2, 8, 4, 12, 20, 24, 6, 27, 3, 32, 5, 48, 7, 64, 9, 18, 36, 28, 40, 10, 56, 14, 72, 22, 80, 11, 81, 13, 96, 15, 54, 21, 108, 30, 88, 26, 104, 34, 112, 17, 128, 19, 144, 23, 160, 25, 50, 75, 100, 44, 52, 60, 68, 76, 84, 92, 116, 120, 38, 136, 42, 135, 33

Offset: 1

Author

Rémy Sigrist, Apr 18 2017

Keywords

• nonn

Comments

This sequence is a permutation of the natural numbers.

Examples

			The first terms, alongside the primes p such that p^4 divides a(n)*a(n+1), are:
n       a(n)    p
--      ----    -
1       1       2
2       16      2
3       2       2
4       8       2
5       4       2
6       12      2
7       20      2
8       24      2
9       6       3
10      27      3
11      3       2
12      32      2
13      5       2
14      48      2
15      7       2
16      64      2
17      9       3
18      18      3
19      36      2
20      28      2
...
165     95      2
166     432     2, 3
167     87      3
...
		

Links

• Rémy Sigrist, Table of n, a(n) for n = 1..10000
• Rémy Sigrist, C++ program for A285386
• Rémy Sigrist, Scatterplot of the first 100000 terms
• Index entries for sequences that are permutations of the natural numbers

Crossrefs

Cf. A285296.